What is the surface area of a cylinder with base radius $2$ and height $7$ ? $2$ $7$
Solution: The areas of the top and the base are simply the area of a circle: $\pi r^2 = \pi \cdot 2^2 = 4 \pi$ The lateral surface area is the same as the area of a rectangle with height $7$ and width equal to the circumference of the base. That circumference is $2 \pi r = 2\pi \cdot 2 = 4\pi$ Thus, the lateral surface area is $wh = 4 \pi \cdot 7 = 28 \pi$ The total surface area is $4 \pi + 4 \pi + 28 \pi = 36\pi$.